Finite Group Databasebeta

← #30600386

Subgroups — #30600386

Order 15616.

784 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2#21461676C211yesmaximal, characteristic, complemented
3C2×#16840620C212yesmaximal, complemented
4#21460697C212yesmaximal, complemented
5#21454163C211yesmaximal, characteristic
6C22×D61⋊C8—21no—
7C2×#14519844C2212yes—
8C2×#14519844C2212yes—
9D61⋊(C4⋊C8)—24no—
10C2×C4⋊#92420—21no—
11C2×#14519834—21no—
12#16840628—21no—
13#16840620—24no—
14C2×#14519773C2211yescharacteristic
15C2×#14519752C411yescharacteristic
16C2×#14519750—21no—
17C2×#14519750—21no—
18C2×#14519748C411yescharacteristic
19C2×C42×D61C2211yescharacteristic
20#16839664C411yescharacteristic
21#16839662—21no—
22#16839662—21no—
23#16839631C2211yescharacteristic
24C61×#390C411yescharacteristic
25C2×D61⋊C8—24no—
26C2×D61⋊C8—42no—
27C2×D61⋊C8—42no—
28C22×#92420—22no—
29C22×#92420—22no—
30#14519844—22no—
31#14519844—22no—
32#14519844—22no—
33#14519844D414yescomplemented
34C4⋊#92420—24no—
35#14519834—42no—
36C22×D244—21no—
37C22×D244C2×C411yescharacteristic
38C22×C22⋊D61—21no—
39C22×C22⋊D61—21no—
40C22×C22⋊D61—21no—
41C22×C4×D61C2×C411yescharacteristic
42C22×C4×D61D411yescharacteristic
43C22×C4×D61D411yescharacteristic
44#14519773—22no—
45#14519773—22no—
46#14519752—42no—
47#14519750—42no—
48#14519750—42no—
49#14519750—42no—
50#14519750—42no—
51#14519748—42no—
52C2×C4⋊Dic61C2×C411yescharacteristic
53C2×#11758196—21no—
54C2×#11758196—21no—
55C2×C22⋊Dic61—21no—
56C2×#11758198—21no—
57C2×#11758198—21no—
58C2×#11758198—21no—
59C2×C4×Dic61D411yescharacteristic
60C2×C4×Dic61D411yescharacteristic
61C2×C4×Dic61C2311yescharacteristic
62C42×D61—22no—
63C42×D61—22no—
64C22×D4×C61C2×C411yescharacteristic
65C2×C4⋊C4×C61C2×C411yescharacteristic
66C2×C22⋊C4×C61—21no—
67C2×C22⋊C4×C61—21no—
68C2×C42×C61C2×C411yescharacteristic
69C24×C61—21no—
70C23×D61—21no—
71C23×D61C22⋊C411yescharacteristic
72C2×D4×C61—22no—
73C2×D4×C61—41no—
74C2×D4×C61—41no—
75C22×C4×C61—21no—
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C22×C411yescharacteristic
79C2×C22⋊D61—42no—
80C2×C22⋊D61—42no—
81C2×C22⋊D61—42no—
82C2×C22⋊D61—41no—
83C2×C22⋊D61—42no—
84C2×C22⋊D61—41no—
85C2×C22⋊D61—41no—
86C2×C22⋊D61—41no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—42no—
90C2×C22⋊D61—41no—
91C2×C22⋊D61—41no—
92C22×Dic61—21no—
93C22×Dic61C22⋊C411yescharacteristic
94C22×Dic61C2×D411yescharacteristic
95C22×Dic61C2×D411yescharacteristic
96C2×D244—22no—
97C2×D244—41no—
98C2×D244—41no—
99C2×D244—42no—
100C2×D244—42no—
101C2×D244—42no—
102C2×C4×D61—21no—
103C2×C4×D61—22no—
104C2×C4×D61—21no—
105C2×C4×D61—22no—
106C2×C4×D61—21no—
107C2×C4×D61—21no—
108C2×C4×D61—22no—
109C2×C4×D61—22no—
110C2×C4×D61—41no—
111C2×C4×D61D812yes—
112C2×C4×D61D812yes—
113C2×C4×D61SD1612yes—
114C2×C4×D61SD1612yes—
115C2×#92420—24no—
116C2×#92420—42no—
117C2×#92420—42no—
118C2×#92420—42no—
119C2×#92420—42no—
120C2×#92420—42no—
121D61⋊C8—48no—
122C4⋊C4×C61—41no—
123C22⋊C4×C61—42no—
124C22⋊C4×C61—42no—
125C42×C61—22no—
126C22⋊Dic61—42no—
127#11758198—42no—
128#11758198—42no—
129#11758198—42no—
130C4⋊Dic61—41no—
131#11758196—41no—
132#11758196—41no—
133#11758196—41no—
134#11758196—41no—
135C4×Dic61—21no—
136C4×Dic61—22no—
137C4×Dic61—21no—
138C4×Dic61C2×D412yes—
139C4×Dic61#4112yes—
140C23×C61—41no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61C2×C22⋊C411yescharacteristic
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—21no—
151C22×D61—21no—
152C22×D61—41no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—41no—
158C22×D61—41no—
159C22×D61#10012yes—
160C22×D61#10212yes—
161C22×D61#10212yes—
162D4×C61—82no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61#10212yes—
173C2×C4×C61#10212yes—
174C2×C4×C61C4×D412yes—
175C22⋊D61—84no—
176C22⋊D61—81no—
177C22⋊D61—81no—
178C22⋊D61—82no—
179C22⋊D61—82no—
180C22⋊D61—81no—
181C22⋊D61—81no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61#12011yescharacteristic
189C2×Dic61#12112yes—
190C2×Dic61#12311yescharacteristic
191C2×Dic61C2×D811yescharacteristic
192C2×Dic61C2×D811yescharacteristic
193C2×Dic61C2×SD1611yescharacteristic
194C2×Dic61C2×SD1611yescharacteristic
195C2×Dic61#13512yes—
196C2×Dic61AGL(1,ℤ/8)11yescharacteristic
197C2×Dic61#13711yescharacteristic
198D244—82no—
199D244—84no—
200C4×D61—22no—
201C4×D61—22no—
202C4×D61—24no—
203C4×D61—24no—
204C4×D61—22no—
205C4×D61—22no—
206C4×D61—44no—
207#92420—44no—
208#92420—82no—
209#9133—611nomaximal, Sylow
210C22×C61—81no—
211C22×C61—81no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61—81no—
216C22×C61—81no—
217C22×C61#38611yescharacteristic
218C22×C61C2×#10011yescharacteristic
219C22×C61#41311yescharacteristic
220C22×C61C2×#10211yescharacteristic
221C22×C61C2×#10211yescharacteristic
222C22×C61#41611yescharacteristic
223C22×C61#41711yescharacteristic
224C2×D61—22no—
225C2×D61—22no—
226C2×D61—22no—
227C2×D61—22no—
228C2×D61—22no—
229C2×D61—22no—
230C2×D61—81no—
231C2×D61—81no—
232C2×D61—81no—
233C2×D61—81no—
234C2×D61—81no—
235C2×D61—81no—
236C2×D61—81no—
237C2×D61#33114yescomplemented
238C4×C61—22no—
239C4×C61—22no—
240C4×C61—22no—
241C4×C61—81no—
242Dic61—41no—
243Dic61—81no—
244Dic61#44711yescharacteristic
245Dic61#44811yescharacteristic
246Dic61#46512yes—
247Dic61#46612yes—
248Dic61#48011yescharacteristic
249Dic61#48111yescharacteristic
250C22×C4⋊C8—611no—
251#2856—611no—
252#1797—611no—
253C2×#331—612no—
254#1296—612no—
255C2×C61—161no—
256C2×C61C2×#33111yescharacteristic
257C2×C61#154011yescharacteristic
258C2×C61#154711yescharacteristic
259C2×C61#155111yescharacteristic
260C2×C61#187411yescharacteristic
261C2×C61#189311yescharacteristic
262C2×C61#190011yescharacteristic
263D61—24no—
264D61—161no—
265C23×C8—1221no—
266C2×#127—611no—
267C2×#121—611no—
268C2×#121—611no—
269C2×#121—1221no—
270C2×#121—1221no—
271C22×C42—611no—
272C2×C4⋊C8—612no—
273C2×C4⋊C8—612no—
274C2×C4⋊C8—1224no—
275C2×C4⋊C8—1221no—
276C2×C22⋊C8—1221no—
277#390—611no—
278#390—1221no—
279#390—1221no—
280#390#692311yescharacteristic
281#384—611no—
282#336—1221no—
283#331—1224no—
284C61#913311yescharacteristic, complemented, Sylow
285C22×D4—611no—
286C22×D4—1221no—
287C22×D4—1221no—
288C22×D4—1221no—
289C22×D4—1221no—
290C22×D4C2×#692311yescharacteristic
291C23×C4—611no—
292C23×C4—611no—
293C23×C4—611no—
294C22×C8—1222no—
295C22×C8—1224no—
296C22×C8—1222no—
297C22×C8—2442no—
298C22×C8—2442no—
299#127—1222no—
300#127—1222no—
301#121—2442no—
302#121—2442no—
303#121—2442no—
304#121—2442no—
305#121—2442no—
306#121—2442no—
307C2×C4⋊C4—611no—
308C2×C4⋊C4—1221no—
309C2×C4⋊C4—1221no—
310C2×C4⋊C4C2×#692311yescharacteristic
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—1221no—
314C2×C22⋊C4—1221no—
315C2×C22⋊C4—1221no—
316C2×C22⋊C4—1221no—
317C2×C42—611no—
318C2×C42—611no—
319C2×C42—611no—
320C2×C42—1222no—
321C2×C42—1222no—
322C2×C42C2×#692311yescharacteristic
323C4⋊C8—614no—
324C4⋊C8—1222no—
325C4⋊C8—1222no—
326C4⋊C8—1222no—
327C4⋊C8—1224no—
328C22⋊C8—2442no—
329C24—21no—
330C24—611no—
331C24—1221no—
332C2×D4—22no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—1222no—
336C2×D4—2441no—
337C2×D4—2441no—
338C2×D4—2442no—
339C2×D4—2442no—
340C2×D4—2442no—
341C2×D4—2441no—
342C2×D4—2441no—
343C2×D4—2441no—
344C2×D4—2441no—
345C2×D4—2441no—
346C2×D4—2442no—
347C2×D4—2441no—
348C2×D4—2442no—
349C2×D4—2441no—
350C2×D4—2441no—
351C2×D4—2442no—
352C2×D4—2442no—
353C2×D4—2442no—
354C22×C4—21no—
355C22×C4—611no—
356C22×C4—611no—
357C22×C4—612no—
358C22×C4—612no—
359C22×C4—612no—
360C22×C4—612no—
361C22×C4—611no—
362C22×C4—1221no—
363C22×C4—1222no—
364C22×C4—1221no—
365C22×C4—1221no—
366C22×C4—1222no—
367C22×C4—1221no—
368C22×C4—1222no—
369C22×C4—1222no—
370C22×C4—1221no—
371C22×C4—2441no—
372C22×C4C22⋊#692311yescharacteristic
373C22×C4C22⋊#692311yescharacteristic
374C22×C4C22×#692311yescharacteristic
375C2×C8—1224no—
376C2×C8—2442no—
377C2×C8—2442no—
378C2×C8—2442no—
379C2×C8—2442no—
380C2×C8—2442no—
381C2×C8—2448no—
382C4⋊C4—41no—
383C4⋊C4—2441no—
384C4⋊C4—2441no—
385C4⋊C4—2441no—
386C4⋊C4—2441no—
387C4⋊C4—2441no—
388C22⋊C4—42no—
389C22⋊C4—42no—
390C22⋊C4—2442no—
391C22⋊C4—2442no—
392C22⋊C4—2442no—
393C22⋊C4—2442no—
394C42—22no—
395C42—612no—
396C42—612no—
397C42—1221no—
398C42—1222no—
399C42—1221no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—612no—
408C23—612no—
409C23—612no—
410C23—1221no—
411C23—1221no—
412C23—1221no—
413C23—1221no—
414C23—2441no—
415C23—2441no—
416C23—2441no—
417C23—2441no—
418C23—2441no—
419C23—2441no—
420C23—2441no—
421C23C2×C22⋊#692311yescharacteristic
422D4—82no—
423D4—4882no—
424D4—4884no—
425D4—4881no—
426D4—4881no—
427D4—4881no—
428D4—4881no—
429D4—4882no—
430D4—4882no—
431D4—4884no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—611no—
442C2×C4—612no—
443C2×C4—611no—
444C2×C4—611no—
445C2×C4—611no—
446C2×C4—611no—
447C2×C4—611no—
448C2×C4—612no—
449C2×C4—611no—
450C2×C4—611no—
451C2×C4—1222no—
452C2×C4—1222no—
453C2×C4—1222no—
454C2×C4—1222no—
455C2×C4—1224no—
456C2×C4—1224no—
457C2×C4—1221no—
458C2×C4—1221no—
459C2×C4—1221no—
460C2×C4—2444no—
461C2×C4—2441no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4#1451983912yes—
465C2×C4#1451983912yes—
466C2×C4D4×#692312yes—
467C8—4882no—
468C8—2444no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—614no—
477C22—1222no—
478C22—1222no—
479C22—1222no—
480C22—1222no—
481C22—1222no—
482C22—1222no—
483C22—4881no—
484C22—4881no—
485C22—4881no—
486C22—4881no—
487C22—4881no—
488C22—4881no—
489C22—4881no—
490C22#1684071011yescharacteristic
491C22D61⋊#10011yescharacteristic
492C22#1684074811yescharacteristic
493C22C2×#1451983911yescharacteristic
494C22C2×#1451983911yescharacteristic
495C22#1684075211yescharacteristic
496C22#1684075311yescharacteristic
497C4—22no—
498C4—22no—
499C4—22no—
500C4—81no—
501C4—611no—
502C4—611no—
503C4—611no—
504C4—611no—
505C4—612no—
506C4—612no—
507C4—4881no—
508C4—2441no—
509C2—161no—
510C2—1224no—
511C2—9761no—
512C2D61⋊#33111yescharacteristic
513C2#2146131611yescharacteristic
514C2#2146133011yescharacteristic
515C2#2146133911yescharacteristic
516C2#2146180611yescharacteristic
517C2#2146183311yescharacteristic
518C2#2146184511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC23×C61C2×C22⋊C4
prime radical#21454163C2
cosocleC2×C4×Dic61C23
hypercenter#390#6923
hypocenterC61#9133
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×D61⋊(C4⋊C8)C2semidirect
2. #21461676C2semidirect
3. C2×#16840620C2semidirect
4. #21460697C2semidirect
33. #14519844D4semidirect
237. C2×D61#331semidirect
284. C61#9133semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D61⋊(C4⋊C8)2
#214616762
C2×#168406202
#214606972
#214541632
#913361